One-Loop QCD and Higgs to Partons Processes Using Six-Dimensional Helicity and Generalized Unitarity

TL;DR

This paper introduces a new six-dimensional helicity and generalized unitarity formalism for calculating one-loop QCD amplitudes, effectively capturing both cut-constructible and rational parts, and applies it to Higgs processes.

Contribution

It combines six-dimensional helicity with D-dimensional unitarity to improve one-loop amplitude computations in QCD, including rational parts often missed by traditional methods.

Findings

Successfully computed four- and five-point one-loop QCD amplitudes.

Demonstrated the method's effectiveness on Higgs plus three gluons at NLO.

Captured both cut-constructible and rational amplitude components.

Abstract

We combine the six-dimensional helicity formalism of Cheung and O'Connell with D-dimensional generalized unitarity to obtain a new formalism for computing one-loop amplitudes in dimensionally regularized QCD. With this procedure, we simultaneously obtain the pieces that are constructible from four-dimensional unitarity cuts and the rational pieces that are missed by them, while retaining a helicity formalism. We illustrate the procedure using four- and five-point one-loop amplitudes in QCD, including examples with external fermions. We also demonstrate the technique's effectiveness in next-to-leading order QCD corrections to Higgs processes by computing the next-to-leading order correction to the Higgs plus three positive-helicity gluons amplitude in the large top-quark mass limit.